As set forth in U.S. Pat. No. 3,631,736, the tooth profiles of gears operating on parallel axes (e.g., cylindrical gears) generally require that the common normal at all points of contact pass through a fixed point on the line of centers, called a pitch point. This is generally a kinematic requirement if one profile is to drive the other at a constant angular speed ratio. A pair of gear profiles contact each other at different positions as the gears rotate. The locus of all possible contact points for a given pair of profiles is called the path of contact. This path of contact is a straight or curved line segment, terminated by the extremities of the gear teeth. The three curves involved in cylindrical gear design are: the profile of the first gear, the profile of the second gear, and the path of contact. Given a fixed center distance and speed ratio, one of these curves may determine the other two. In particular, if the path of contact is shown as a given curve, then the profiles of both gears may be uniquely determined.
For cylindrical gear applications, the gear set may include a first gear with a first profile, a first center point, and a first outside radius (from the first center point to the perimeter of the first gear) and a second gear with a second profile, a second center point, and a second outside radius (from the second center point to the perimeter of the second gear). Pitch radii are the distances between the pitch point and the respective gear centers (i.e., the first center point and the second center point). In other words, the pitch radii specify the distance between the pitch point and the respective gear axis. As the first and second gears rotate, the profile curves of the first and second gears will contact each other at different positions and the locus of all successive contact points determine the shape of the path of contact (e.g., line of action).
Each contact point may be indicated in terms of polar coordinates as being located at a certain distance from the pitch point and at a certain angle which is also the pressure angle from a horizontal line normal to the line connecting the first and second center points. The first and second profiles for the gears may have first and second radii of curvature, respectively, with first and second lengths.
It may be desirable to use tooth flank geometry of a first and second gear (e.g., a pinion gear and a side gear in a differential) to cause movement of a plane of action defining contact points between the tooth flank of a first gear and the tooth flank of a second gear in a predetermined and/or controlled manner.